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Muon-spin-relaxation measurements have been performed for the partiallyZn-substituted La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ with y=0-0.10 in the overdopedregime up to x=0.30. In the 3 % Zn-substituted samples up to x=0.27,exponential-like depolarization of muon spins has been observed at lowtemperatures, indicating Zn-induced slowing-down of the Cu-spin fluctuations.The depolarization rate decreases with increasing x and almost no fastdepolarization of muon spins has been observed for x=0.30 wheresuperconductivity disappears. The present results suggest that the dynamicalstripe correlations exist in the whole superconducting regime ofLa_2-x_Sr_x_CuO_4_ and that there is no quantum critical point at x~0.19.

Cu-spin dynamics in the overdoped regime of La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ probed by muon spin relaxation